A straight Line depends on your geometric point of view.
… keep those hypocycloids rolling, rawhide!
In addition to animated gifs showing the hypocycloids, there’s a short explanation of symmetry groups, which is important in physics, especially in understanding spin states and quarks.
Our World: Rates of Cancer Approach Historic High
Mathematically Literate World: Rates of Surviving Long Enough to Develop Cancer Approach Historic High
Draw a straight line, and then continue it for the same length but deflected by an angle. If you continue doing this you will eventually return to roughly where you started, having drawn out an approximation to a circle. But what happens if you increase the angle of deflection by a fixed amount at each step?
How big is infinity? Most people, though familiar with the general concept of infinity, would probably answer with a simple, question-dodging response of “infinite.” To be fair, the infinite is a really difficult concept to wrap one’s head around, and still causes challenges and puzzles in mathematics to this day.
You probably use a descendant of Fourier’s idea every day, whether you’re playing an MP3, viewing an image on the web, asking Siri a question, or tuning in to a radio station.
I linked to the drawing of Homer Simpson’s face before, but didn’t explain Fourier series/transforms in as much depth (or as well)
I have no problem with the viewpoint that math instruction needs to improve, and that covering a lot of ground but only superficially is a bad idea. Plus all the standardized testing idiocy.
But I disagree with the “math should be an elective after grade 8” proposal. The point is not, as is suggested, to churn out a bunch of math majors. Math is the language of science, and people need to be math and scientifically literate — that’s why they should be taught math and science. If you don’t teach math, not teaching science necessarily follows. And there is no way to teach some science any way but superficially without math.
One could easily replace the math examples in that section with English and Shakespeare (or fill in your favorite novels), and much of it would read pretty much the same, and I don’t think that’s a selling point of the argument. The point of teaching English and Shakespeare is not because we expect all of our students to become literature majors in college. They take English because they have to be able to communicate effectively, and they study Shakespeare because culture is important, too. If people understood that math is a language, I think it would blunt some of these arguments. You don’t hear people arguing that little Timmy/Sally “isn’t wired for English” as an excuse for trying to get it out of the curriculum. Understanding math and science adds value to how one gives context to information and how one interacts with the world. It’s a necessary part of education.
Lake Wobegon, where all the women are strong, all the men are good looking, and all the children are above average
What are the odds of being normal?
I think a better word here would be typical in the way that Bee is using it, but that really doesn’t change the thrust of the discussion. The really short version is that if the typical family has 2.3 children, then nobody is typical.
It’s interesting, I think, this mix of “I’m average” is some ways of thinking and “I’m above average” in others, and the Wikipedia article included in the link does (as I expected) discuss the Dunning-Kruger effect as part of overestimating our abilities. Though I expect that works in reverse, too: people thinking they are typical in some way when they aren’t, like that guy who ran for president last year (Mitch Rumbly?) who tried to portray himself as a regular guy and failing pretty miserably. (But that’s politics, so we don’t know how much of that is pretend)
However, this is something that I have thought about and never formed it into a blog post, but (as so often happens) now that I have a catalyst I will make a few comments. Or just ramble.
Not only do we think of ourselves as average or typical in many respects, I think we view experiences as being typical as well. Consider buying some widget or gizmo, as a first-time customer of ACME, and finding that it has some flaw. It doesn’t really matter if ACME has 99.99% positive quality control on their gizmos, and you were just unlucky enough to get that 10,000th unit off the line that’s faulty — there’s a decent chance you’ll just say that ACME sucks, thinking that this happens to everyone. Same thing for getting poor treatment at customer service. It doesn’t matter to you that you’re unlikely to be treated poorly if a second chance came up, because you won’t give the company that chance. (and I’m guessing there’s some neuroscience description of all this I know nothing about, because I’m a physicist and not a neuroscientist.)
The bottom line is we’re bad at assessing probability and risk for unusual events because see them as being more typical than they really are. It’s also something that many (or at least some) companies realize, so they work hard at not losing you with a first-time bad experience, or giving you a common experience that’s better than their competitors (like with customer service, or when visiting a restaurant, etc), and also fed by the news, which reports unusual events but not mundane ones.